Photoactivation systems and methods for corneal cross-linking treatments

ABSTRACT

A system for treating an eye includes a laser light source providing photoactivating light. The system includes a scanning system to receive the photoactivating light as a laser beam and to move the laser beam over a cornea treated with a cross-linking agent. The system includes a controller that provides control signal(s) to programmatically control the laser light source and the scanning system. The control signal(s) cause the laser beam to visit region(s) of the cornea more than once according to a scan pattern and expose the region(s) to the photoactivating light. The photoactivating light causes the cross-linking agent in the exposed region(s) to react with oxygen to generate cross-linking activity in the exposed region(s). The scan pattern causes a predetermined period of time to pass between visits by the laser beam to the exposed region(s), the predetermined period of time allowing oxygen in the exposed region(s) to replenish.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/987,370, filed Aug. 6, 2020, claiming priority to, and the benefitof, U.S. Provisional Patent Application No. 62/883,197, filed Aug. 6,2019, the contents of which are incorporated entirely herein byreference and relied upon.

BACKGROUND Field

The present disclosure pertains to systems and methods for eyetreatments, and more particularly, to systems and methods forphotoactivating a cross-linking agent.

Description of Related Art

Cross-linking treatments may be employed to treat eyes suffering fromdisorders, such as keratoconus. In particular, keratoconus is adegenerative disorder of the eye in which structural changes within thecornea cause it to weaken and change to an abnormal conical shape.Cross-linking treatments can strengthen and stabilize areas weakened bykeratoconus and prevent undesired shape changes.

Cross-linking treatments may also be employed after surgical procedures,such as Laser-Assisted in situ Keratomileusis (LASIK) surgery. Forinstance, a complication known as post-LASIK ectasia may occur due tothe thinning and weakening of the cornea caused by LASIK surgery. Inpost-LASIK ectasia, the cornea experiences progressive steepening(bulging). Accordingly, cross-linking treatments can strengthen andstabilize the structure of the cornea after LASIK surgery and preventpost-LASIK ectasia.

Cross-linking treatments may also be employed to induce refractivechanges in the cornea to correct disorders such as myopia, hyperopia,astigmatism, irregular astigmatism, presbyopia, etc.

SUMMARY

Embodiments include systems and methods for photoactivating across-linking agent in corneal cross-linking treatments. Using a laserlight source to achieve a scanned light pattern can provide advantagesfor photoactivating a cross-linking agent. In particular, scanningparameters for the laser can be optimized to increase the efficacy ofindividual treatments. For instance, treatment time, total dose,intensity/irradiance of the laser beam, pulsing of the laser beam, sizeof the spot defined by the laser beam (laser spot size), velocity orduration of application of the laser spot, and/or frequency ofrepetition of portions of the scan pattern can be controlled to enhancecross-linking activity. Such parameters can be optimized according tothe photochemical kinetic reactions involved in cross-linking activityas described above. These reactions determine the consumption andreplenishment of oxygen during cross-linking activity, supply andphoto-degradation of the cross-linking agent molecules, and depth ofeffect.

According to an example embodiment, a system for treating an eyeincludes a laser light source configured to provide photoactivatinglight. The system includes a scanning system configured to receive thephotoactivating light as a laser beam and to move the laser beam over acornea treated with a cross-linking agent. The system includes acontroller configured to provide control signals to programmaticallycontrol the laser light source and the scanning system. The one or morecontrol signals causing the laser beam to visit one or more regions ofthe cornea more than once according to a scan pattern and expose the oneor more regions to the photoactivating light. The photoactivating lightcauses the cross-linking agent in the one or more exposed regions toreact with oxygen to generate cross-linking activity in the one or moreexposed regions. The scan pattern causes a predetermined period of timeto pass between visits by the laser beam to the one or more exposedregions, the predetermined period of time allowing oxygen in the one ormore exposed regions to replenish and allow a desired amount of thecross-linking activity to be generated with sufficient oxygen duringeach visit to the one or more exposed regions.

According to another example embodiment, a method for treating an eyeincludes generating photoactivating light with a laser light source. Themethod includes directing the photoactivating light as a laser beam to ascanning system. The method includes operating the scanning system tocause the laser beam to move over the cornea and visit one or moreregions of the cornea more than once according to a scan pattern andexpose the one or more regions to the photoactivating light. Thephotoactivating light causes the cross-linking agent in the one or moreexposed regions to react with oxygen to generate cross-linking activityin the one or more exposed regions. The method includes optimizing thescan pattern to cause a predetermined period of time to pass betweenvisits by the laser beam to the one or more exposed regions, thepredetermined period of time allowing oxygen in the one or more exposedregions to replenish and allow a desired amount of the cross-linkingactivity to be generated with sufficient oxygen during each visit to theone or more exposed regions.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example system that delivers a cross-linking agentand photoactivating light to a cornea of an eye in order to generatecross-linking of corneal collagen, according to aspects of the presentdisclosure.

FIG. 2A illustrates an example circular treatment pattern that can beproduced with a XY scanning mirror pair.

FIG. 2B illustrates an example annular treatment pattern that that canalso be produced with a XY scanning mirror pair.

FIG. 3 illustrates an example treatment system that provides alaser-based approach for projecting patterns of photoactivating light toa cornea employing a XY scanning system, according to aspects of thepresent disclosure.

FIG. 4A illustrates an example treatment zone where a laser beam has aspot size with a diameter that is sufficiently large to applyphotoactivating light in a spiral to 100% of an area defined by asubstantially circular boundary, according to aspects of the presentdisclosure.

FIG. 4B illustrates another example treatment zone where a laser beamhas a spot size with a diameter that is 50% of the diameter shown inFIG. 4A, according to aspects of the present disclosure.

FIG. 4C illustrates yet another example treatment zone where a laserbeam has a spot size with a diameter that is 25% of the diameter shownin FIG. 4A, according to aspects of the present disclosure.

FIG. 5 illustrates a flowchart for an example process for optimizinglaser scanning parameters for cross-linking treatments, according toaspects of the present disclosure.

FIG. 6 illustrates an example repetition cycle for laser scanning in across-linking treatment, according to aspects of the present disclosure.

FIG. 7 illustrates oxygen concentration and fluorescent intensityassociated with the cross-linking agent at a location during an examplecross-linking treatment employing laser scanning, according to aspectsof the present disclosure.

FIGS. 8A-E illustrate curvature change resulting from treatments of fiveeyes where the epithelium layer is left on the eye (epi-on), accordingto aspects of the present disclosure.

FIGS. 9A-E illustrate curvature change resulting from treatments of fiveeyes where the epithelium layer is entirely removed (epi-off), accordingto aspects of the present disclosure.

FIG. 10 illustrates aspects of an example scan pattern defined bydiscrete dots applied according to a grid inside a boundary defining atreatment zone, according to aspects of the present disclosure.

FIG. 11 illustrates different example combinations of parameter valuesfor laser scanning applying discrete dots according to a grid inside aboundary defining a treatment zone, according to aspects of the presentdisclosure.

FIGS. 12A-C illustrate example time series of scanner position graphsfor implementations of the combination of the treatment parameters shownin row B of FIG. 11 using different respective values for maximum traveldistance (MTD), according to aspects of the present disclosure.

FIG. 13 illustrates a delay between eye position and delivery ofphotoactivating light due to discrete-time detection of the eye andfinite response time of a treatment system, according to aspects of thepresent disclosure.

FIG. 14 illustrates an example approach for accounting for locationerror in a modified grid-based point and shoot approach, according toaspects of the present disclosure.

FIG. 15 illustrates an example raster scanning pattern, according toaspects of the present disclosure.

FIG. 16 illustrates an example zig-zag scanning pattern, according toaspects of the present disclosure.

FIG. 17 illustrates an example treatment system that provides alaser-based approach for projecting patterns of photoactivating light toa cornea employing a diffractive multi-beam splitter, according toaspects of the present disclosure.

FIG. 18 illustrates an example treatment system that provides alaser-based approach for projecting patterns of photoactivating light toa cornea employing a diffractive beam shaper, according to aspects ofthe present disclosure.

FIG. 19A illustrates an example annular treatment pattern with an outerdiameter of approximately 4 mm, produced by pulsing a laser beam at a50% duty cycle and a fixed pulse frequency over a spiral tracing,according to aspects of the present disclosure.

FIG. 19B illustrates an example annular treatment pattern with an outerdiameter of approximately 8 mm, produced by pulsing a laser beam at a50% duty cycle and a fixed pulse frequency over a spiral tracing,according to aspects of the present disclosure.

FIG. 20A illustrates an example annular treatment pattern with an outerdiameter of approximately 4 mm, produced by pulsing a laser beam at a50% duty cycle and a variable pulse frequency over a spiral tracing,according to aspects of the present disclosure.

FIG. 20B illustrates an example annular treatment pattern with an outerdiameter of approximately 8 mm, produced by pulsing a laser beam at a50% duty cycle and a variable pulse frequency over a spiral tracing,according to aspects of the present disclosure.

FIG. 20C illustrates an example annular treatment pattern with an outerdiameter of approximately 9 mm, produced by a laser beam with variablepulse frequency, according to aspects of the present disclosure.

FIG. 21 illustrates example waveforms for driving a galvanometer as wellas a laser modulation waveform during a portion of a treatment employinglaser scanning, according to aspects of the present disclosure.

FIG. 22A illustrates example waveforms for driving a galvanometer duringa complete treatment, according to aspects of the present disclosure.

FIG. 22B illustrates a laser modulation waveform for the treatment ofFIG. 22A, according to aspects of the present disclosure.

FIG. 23 illustrates an example laser modulation waveform split intomultiple radial zones, according to aspects of the present disclosure.

FIG. 24A illustrates an example annular treatment pattern with an outerdiameter of approximately 4 mm, produced with a pulsed laser beamscanned with variable laser modulation frequency implementing a lasermodulation waveform split into multiple radial zones based on amodulation frequency limit, according to aspects of the presentdisclosure.

FIG. 24B illustrates the example laser modulation waveform split intomultiple radial zones based on a modulation frequency limit for thetreatment of FIG. 24A, according to aspects of the present disclosure.

FIG. 25A illustrates an example annular treatment pattern with an outerdiameter of approximately 9 mm, produced with a pulsed laser beamscanned with variable laser modulation frequency implementing a lasermodulation waveform split into multiple radial zones based on amodulation frequency limit, according to aspects of the presentdisclosure.

FIG. 25B illustrates the example laser modulation waveform split intomultiple radial zones based on a modulation frequency limit for thetreatment of FIG. 25A, according to aspects of the present disclosure.

FIG. 26A illustrates an example annular treatment pattern 2600 a with anouter diameter of approximately 9 mm produced with a pulsed laser beamscanned with variable laser modulation frequency implementing a lasermodulation waveform with one radial zone based on a modulation frequencylimit, according to aspects of the present disclosure.

FIG. 26B illustrates the example laser modulation waveform with oneradial zone based on a modulation frequency limit for the treatment ofFIG. 25A, according to aspects of the present disclosure.

FIG. 27 illustrates aspects of a spot profile produced by a pulsed laserbeam traveling along a scan, according to aspects of the presentinvention.

FIG. 28A illustrates a Gaussian laser spot with a laser modulationfrequency of 25 kHz, according to aspects of the present invention.

FIG. 28B illustrates a Gaussian laser spot with a laser modulationfrequency of 50 kHz, according to aspects of the present invention.

FIG. 28C illustrates a Gaussian laser spot with a laser modulationfrequency of 75 kHz, according to aspects of the present invention.

FIG. 28D illustrates a Gaussian laser spot with a laser modulationfrequency of 100 kHz, according to aspects of the present invention.

While the present disclosure is susceptible to various modifications andalternative forms, a specific embodiment thereof has been shown by wayof example in the drawings and will herein be described in detail. Itshould be understood, however, that it is not intended to limit thepresent disclosure to the particular forms disclosed, but on thecontrary, the intention is to cover all modifications, equivalents, andalternatives falling within the spirit of the present disclosure.

DESCRIPTION

FIG. 1 illustrates an example treatment system 100 for generatingcross-linking of collagen in a cornea 2 of an eye 1. The treatmentsystem 100 includes an applicator 132 for applying a cross-linking agent130 to the cornea 2. In example embodiments, the applicator 132 may bean eye dropper, syringe, or the like that applies the photosensitizer130 as drops to the cornea 2. Example systems and methods for applyingthe cross-linking agent are described in U.S. Patent ApplicationPublication No. 2017/0296383, filed Apr. 13, 2017 and titled “Systemsand Methods for Delivering Drugs to an Eye,” the contents of which areincorporated entirely herein by reference.

The cross-linking agent 130 may be provided in a formulation that allowsthe cross-linking agent 130 to pass through the corneal epithelium 2 aand to underlying regions in the corneal stroma 2 b (also known as an“epi-on” procedure). Alternatively, the corneal epithelium 2 a may beremoved or otherwise incised to allow the cross-linking agent 130 to beapplied more directly to the underlying tissue (also known as an“epi-off” procedure).

The treatment system 100 includes an illumination system with a lightsource 110 and optical elements 112 for directing light to the cornea 2.In some embodiments, the light source 110 may include a light emittingdiode (LED). In other embodiments, the light source 110 may provide alaser. The light causes photoactivation of the cross-linking agent 130to generate cross-linking activity in the cornea 2. For example, thecross-linking agent may include riboflavin and the photoactivating lightmay include ultraviolet A (UVA) (e.g., approximately 365 nm or 375 nm,or a wavelength falling within the band of 315 nm to 400 nm) light.Alternatively, the photoactivating light may include another wavelength,such as a visible wavelength (e.g., approximately 452 nm) or any otherwavelength selected to activate a photosensitizing agent. As describedfurther below, corneal cross-linking improves corneal strength bycreating chemical bonds within the corneal tissue according to a systemof photochemical kinetic reactions.

Riboflavin and the photoactivating light may be applied to stabilizeand/or strengthen corneal tissue to address corneal ectatic disorders,such as keratoconus or post-LASIK ectasia. The application of riboflavinand the photoactivating light may also allow for various amounts ofrefractive correction, which for instance, may involve combinations ofmyopia, hyperopia, astigmatism, irregular astigmatism, presbyopia andcomplex corneal refractive surface corrections due to corneal ectaticdisorders as well as other conditions of corneal biomechanicalalteration/degeneration, etc.

The treatment system 100 includes one or more controllers 120 thatcontrol aspects of the treatment system 100, including the light source110 and/or the optical elements 112. In an implementation, the cornea 2can be more broadly treated with the cross-linking agent 130 (e.g., withan eye dropper, syringe, etc.), and the photoactivating light from thelight source 110 can be selectively directed to regions of the treatedcornea 2 according to a particular pattern.

The optical elements 112 may include one or more mirrors, lenses, orother optical components for directing and focusing the photoactivatinglight emitted by the light source 110 to a particular pattern on thecornea 2. The optical elements 112 may further include filters forpartially blocking wavelengths of light emitted by the light source 110and for selecting particular wavelengths of light to be directed to thecornea 2 for photoactivating the cross-linking agent 130. In addition,the optical elements 112 may include one or more beam splitters fordividing a beam of light emitted by the light source 110, and mayinclude one or more optical sinks for absorbing light emitted by thelight source 110. The optical elements 112 may also accurately andprecisely focus the photo-activating light to particular focal planeswithin the cornea 2, e.g., at a particular depths in the underlyingregion 2 b where cross-linking activity is desired.

According to some aspects, optical elements of an example treatmentsystem may employ fiber-optic elements. The use of fiber-optic elementscan eliminate the need for free space optical elements as well asopto-mechanical mounts in a treatment system. Advantageously, the use offiber-optics can reduce the size and footprint of a treatment system,reduce design and manufacturing complexity and cost, and enhancereliability.

Moreover, specific regimes of the photoactivating light can be modulatedto achieve a desired degree of cross-linking in the selected regions ofthe cornea 2. The one or more controllers 120 may be used to control theoperation of the light source 110 and/or the optical elements 112 toprecisely deliver the photoactivating light according to any combinationof: wavelength, bandwidth, intensity, power, location, depth ofpenetration, and/or duration of treatment (the duration of the exposurecycle, the dark cycle, and the ratio of the exposure cycle to the darkcycle duration).

The parameters for photoactivation of the cross-linking agent 130 can beadjusted, for example, to reduce the amount of time required to achievethe desired cross-linking. In an example implementation, the time can bereduced from minutes to seconds. While some configurations may apply thephotoactivating light at an irradiance of 5 mW/cm², larger irradiance ofthe photoactivating light, e.g., multiples of 5 mW/cm², can be appliedto reduce the time required to achieve the desired cross-linking. Thetotal dose of energy absorbed in the cornea 2 can be described as aneffective dose, which is an amount of energy absorbed through an area ofthe corneal epithelium 2 a. For example the effective dose for a regionof the corneal surface 2A can be, for example, 5 J/cm², or as high as 20J/cm² or 30 J/cm². The effective dose described can be delivered from asingle application of energy, or from repeated applications of energy.

The optical elements 112 of the treatment system 100 may include amicroelectromechanical system (MEMS) device, e.g., a digitalmicro-mirror device (DMD), to modulate the application ofphotoactivating light spatially and temporally. Using DMD technology,the photoactivating light from the light source 110, e.g., an LED, isprojected in a precise spatial pattern that is created bymicroscopically small mirrors laid out in an array on a semiconductorchip. Each mirror represents one or more pixels in the pattern ofprojected light. With the DMD one can perform topography guidedcross-linking. The control of the DMD according to topography may employseveral different spatial and temporal irradiance and dose profiles. Asdescribed further below, these spatial and temporal dose profiles may becreated using continuous wave (CW) illumination but may also bemodulated via pulsed illumination by pulsing the illumination sourceunder varying frequency and duty cycle regimes. Alternatively, the DMDcan modulate different frequencies and duty cycles on a pixel by pixelbasis to give ultimate flexibility using continuous wave illumination.Or alternatively, both pulsed illumination and modulated DMD frequencyand duty cycle combinations may be combined. This allows for specificamounts of spatially determined corneal cross-linking. This spatiallydetermined cross-linking may be combined with dosimetry, interferometry,optical coherence tomography (OCT), corneal topography, etc., forpre-treatment planning and/or real time monitoring and modulation ofcorneal cross-linking during treatment. Additionally, pre-clinicalpatient information may be combined with finite element biomechanicalcomputer modeling to create patient specific pre-treatment plans.

To control aspects of the delivery of the photoactivating light,embodiments may also employ aspects of multiphoton excitationmicroscopy. In particular, rather than delivering a single photon of aparticular wavelength to the cornea 2, the treatment system 100 maydeliver multiple photons of longer wavelengths, i.e., lower energy, thatcombine to initiate the cross-linking. Advantageously, longerwavelengths are scattered within the cornea 2 to a lesser degree thanshorter wavelengths, which allows longer wavelengths of light topenetrate the cornea 2 more efficiently than light of shorterwavelengths. Shielding effects of incident irradiation at deeper depthswithin the cornea are also reduced over conventional short wavelengthillumination since the absorption of the light by the photosensitizer ismuch less at the longer wavelengths. This allows for enhanced controlover depth specific cross-linking. For example, in some embodiments, twophotons may be employed, where each photon carries approximately halfthe energy necessary to excite the molecules in the cross-linking agent130 to generate the photochemical kinetic reactions described furtherbelow. When a cross-linking agent molecule simultaneously absorbs bothphotons, it absorbs enough energy to release reactive radicals in thecorneal tissue. Embodiments may also utilize lower energy photons suchthat a cross-linking agent molecule must simultaneously absorb, forexample, three, four, or five, photons to release a reactive radical.The probability of the near-simultaneous absorption of multiple photonsis low, so a high flux of excitation photons may be required, and thehigh flux may be delivered through a femtosecond laser.

A large number of conditions and parameters affect the cross-linking ofcorneal collagen with the cross-linking agent 130. For example, theirradiance and the dose of photoactivating light affect the amount andthe rate of cross-linking. The UVA light may be applied continuously(CW) or as pulsed light, and this selection has an effect on the amount,the rate, and the extent of cross-linking. If the UVA light is appliedas pulsed light, the duration of the exposure cycle, the dark cycle, andthe ratio of the exposure cycle to the dark cycle duration have aneffect on the resulting corneal stiffening. Pulsed light illuminationcan be used to create greater or lesser stiffening of corneal tissuethan may be achieved with continuous wave illumination for the sameamount or dose of energy delivered. Light pulses of suitable length andfrequency may be used to achieve more optimal chemical amplification.For pulsed light treatment, the on/off duty cycle may be betweenapproximately 1000/1 to approximately 1/1000; the irradiance may bebetween approximately 1 mW/cm² to approximately 1000 mW/cm² averageirradiance, and the pulse rate may be between approximately 0.01 HZ toapproximately 1000 Hz or between approximately 1000 Hz to approximately100,000 Hz.

The treatment system 100 may generate pulsed light by employing a DMD,electronically turning the light source 110 on and off, and/or using amechanical or opto-electronic (e.g., Pockels cells) shutter ormechanical chopper or rotating aperture. Because of the pixel specificmodulation capabilities of the DMD and the subsequent stiffness impartedbased on the modulated frequency, duty cycle, irradiance and dosedelivered to the cornea, complex biomechanical stiffness patterns may beimparted to the cornea. A specific advantage of the DMD system andmethod is that it allows for randomized asynchronous pulsed topographicpatterning, creating a non-periodic and uniformly appearing illuminationwhich eliminates the possibility for triggering photosensitive epilepticseizures or flicker vertigo for pulsed frequencies between 2 Hz and 84Hz.

Although example embodiments may employ stepwise on/off pulsed lightfunctions, it is understood that other functions for applying light tothe cornea may be employed to achieve similar effects. For example,light may be applied to the cornea according to a sinusoidal function,sawtooth function, or other complex functions or curves, or anycombination of functions or curves. Indeed, it is understood that thefunction may be substantially stepwise where there may be more gradualtransitions between on/off values. In addition, it is understood thatirradiance does not have to decrease down to a value of zero during theoff cycle, and may be above zero during the off cycle. Desired effectsmay be achieved by applying light to the cornea according to a curvevarying irradiance between two or more values.

Examples of systems and methods for delivering photoactivating light aredescribed, for example, in U.S. Patent Application Publication No.2011/0237999, filed Mar. 18, 2011 and titled “Systems and Methods forApplying and Monitoring Eye Therapy,” U.S. Patent ApplicationPublication No. 2012/0215155, filed Apr. 3, 2012 and titled “Systems andMethods for Applying and Monitoring Eye Therapy,” and U.S. PatentApplication Publication No. 2013/0245536, filed Mar. 15, 2013 and titled“Systems and Methods for Corneal Cross-Linking with Pulsed Light,” thecontents of these applications being incorporated entirely herein byreference. Embodiments may generate cross-linking activity in the corneaaccording to circular and/or annular patterns defined by the delivery ofphotoactivating light (e.g., via the DMD described above). Additionallyor alternatively, embodiments may generate cross-linking activity in thecornea according to non-circular and/or non-annular patterns defined bythe delivery of photoactivating light (e.g., via the DMD).

Patterns of photoactivating light can be applied (e.g., via the DMD) tothe eye in separate treatment zones with different doses sequentially orcontinuously applied. For instance, one treatment zone can be “turnedoff” (i.e., delivery of the corresponding photoactivating light ceases)while another “stays on” (i.e., delivery of the correspondingphotoactivating light continues). The treatment zones can be, forinstance, annularly shaped about a center point of the eye. There mayalso be discontinuous zones where no the photoactivating light isapplied (e.g., a central treatment zone surrounded by an annulus of nolight surrounded by an annular treatment zone of light, etc.). Thewidths of the annular zones can be of different dimensions, e.g., oneannular zone has a width of 1 mm and another has a width of 2 mm.Applying the photoactivating light in annular treatment zones on theperiphery of the eye without a central treatment zone can result in ahyperopic correction, for instance, by causing the central region of theeye to have an increased curvature while the periphery is strengthened.In some cases, central and surrounding treatment zones can be ellipticalin shape, for instance to address astigmatism, by preferentiallygenerating cross-linking activity in regions of the cornea to correctthe astigmatism. Such elliptically shaped annular treatment zones arepreferentially oriented with the axis of the annular treatment zonesaligned according to the orientation of the astigmatism. Theelliptically shaped treatment zones can also be irregularly asymmetric(i.e., having major and minor axis that are not perpendicular and can besituated with distinct center points (centers of mass)).

Cross-linking treatments can be tuned according to one or morebiomechanical properties of the eye, such as the corneal topography(i.e., shape), corneal strength (i.e., stiffness), and/or cornealthickness. Optical correction and/or strengthening of the cornea can beachieved by applying the cross-linking agent and/or photoactivatinglight in one or more iterations with adjustable characteristics for eachiteration. Generally, a developed treatment plan can include a number ofapplications of the cross-linking agent, the amount and concentration ofthe cross-linking agent for each application, the number of applicationsof photoactivating light, and the timing, duration, power, energydosage, and pattern of the photoactivating light for each application.Furthermore, the cross-linking treatments can be adapted based onfeedback information relating to the biomechanical properties gatheredin real time during treatment or during breaks in treatments.

When riboflavin absorbs radiant energy, especially light, it undergoesphotoactivation. There are two photochemical kinetic pathways forriboflavin photoactivation, Type I and Type II. The reactions involvedin both the Type I and Type II mechanisms and other aspects of thephotochemical kinetic reactions generating cross-linking activity aredescribed in U.S. Pat. No. 10,350,111, filed Apr. 27, 2016 and titled“Systems and Methods for Cross-Linking Treatments of an Eye,” thecontents of which are incorporated entirely herein by reference.

Corneal cross-linking reactions are rate limited by oxygenconcentrations in the corneal tissue. Thus, the addition of oxygen alsoaffects the amount of corneal cross-linking. In human tissue, O₂ contentis very low compared to the atmosphere. The rate of cross-linking in thecornea, however, is related to the concentration of O₂ when it isirradiated with photoactivating light. Therefore, it may be advantageousto increase or decrease the concentration of O₂ actively duringirradiation to control the rate of cross-linking until a desired amountof cross-linking is achieved. Oxygen may be applied during thecross-linking treatments in a number of different ways. One approachinvolves supersaturating the riboflavin with O₂. Thus, when theriboflavin is applied to the eye, a higher concentration of O₂ isdelivered directly into the cornea with the riboflavin and affects thereactions involving O₂ when the riboflavin is exposed to thephotoactivating light. According to another approach, a steady state ofO₂ (at a selected concentration) may be maintained at the surface of thecornea to expose the cornea to a selected amount of O₂ and cause O₂ toenter the cornea. As shown in FIG. 1 , for instance, the treatmentsystem 100 also includes an oxygen source 140 and an oxygen deliverydevice 142 that optionally delivers oxygen at a selected concentrationto the cornea 2. Example systems and methods for applying oxygen duringcross-linking treatments are described, for example, in U.S. Pat. No.8,574,277, filed Oct. 21, 2010 and titled “Eye Therapy,” U.S. PatentApplication Publication No. 2013/0060187, filed Oct. 31, 2012 and titled“Systems and Methods for Corneal Cross-Linking with Pulsed Light,” thecontents of these applications being incorporated entirely herein byreference. Additionally, an example mask device for deliveringconcentrations of oxygen as well as photoactivating light in eyetreatments is described in U.S. Patent Application Publication No.2017/0156926, filed Dec. 3, 2016 and titled “Systems and Methods forTreating an Eye with a Mask Device,” the contents of which areincorporated entirely herein by reference. For instance, a mask may beplaced over the eye(s) to produce a consistent and known oxygenconcentration above the surface.

As described above, the treatment system 100 includes optical elements112 that direct light (e.g., UV light) from a light source 110 tophotoactivate the cross-linking agent 130 (e.g., riboflavin) applied tothe cornea 2 and thus generate cross-linking activity. In particular,the photoactivating light can be selectively directed to regions of thecornea 2 according to a particular spatial treatment pattern. In someembodiments, a treatment system can provide an adjustable treatmentpattern so that different ophthalmic conditions can be treated with thesame treatment system.

Example treatment systems that treat different ophthalmic conditions byproviding different treatment patterns are described in U.S. PatentApplication Publication No. 2020/0107953, filed Oct. 9, 2019 and titled“Photoactivation Systems and Methods for Corneal Cross-LinkingTreatments,” the contents of these application being incorporatedentirely herein by reference.

Scanning Treatment Systems

Optical elements of an example treatment system include a XY scanningmirror pair (e.g., instead of a DMD) that can scan a UV light beam toform a UV light pattern with a small, high-quality spot. (The depth ofthe cornea is measured along a z-axis and patterns of photoactivatinglight may be projected on transverse x-y planes.) For instance, FIG. 2Aillustrates an example circular treatment pattern 200 a that can beproduced with a XY scanning mirror pair. FIG. 2B illustrates an exampleannular treatment pattern 200 b that that can also be produced with a XYscanning mirror pair.

FIG. 3 illustrates an example scanning treatment system 300. Thetreatment system 300 includes a UV (e.g., UVA) laser source 310 and agalvanometer mirror system (or dual-axis MEMS mirror) 312 that acts as aXY scanning system. The laser source 310 may employ a xenon fluoride(XeF) excimer laser, femtosecond pulse laser, or a laser diode. Thelaser source 310 may be implemented with a light amplitude modulator(either internal or external to the laser source 310). The treatmentsystem 300 includes a controller 320 that may control aspects of thetreatment system 300. In particular, the controller 320 can trigger thelaser source 310 to deliver a laser beam in pulses as described above.

The laser beam from the laser source 310 produces a small, high-qualityspot on the galvanometer mirror system 312. The galvanometer mirrorsystem 312 includes a X mirror 312 a that can scan the UV light beam inthe x-direction and a Y mirror 312 b that can scan the UV light beam inthe y-direction. The controller 320 can control the galvanometer mirrorsystem 312 to scan the laser beam in the x- and y-directions accordingto a predefined scan pattern 10. The scan pattern 10 can be translatedto cause the X mirror 312 a and the Y mirror 312 b to scan the laserbeam in the x- and y-directions, respectively. In particular, thecontroller 320 can transmit a X position signal to the X mirror 312 a tocontrol a tilt angle of the X mirror 312 a and direct the laser beam toa desired position along the x-axis. Correspondingly, controller 320 cantransmit a Y position signal to the Y mirror 312 b to control a tiltangle of the Y mirror 312 b and direct the laser beam to a desiredposition along the y-axis. The treatment system 300 also includes a lens314 (e.g., a telecentric, f-theta, or other scanning lens) thattransmits the scanned laser beam to the cornea 2. Additionally oralternatively, a lens may be positioned between the laser 310 and the Xmirror 312 a. Light from the laser source 310 may be transmitted viafree space or may be coupled to an optical fiber for transmission to thevicinity of the galvanometer mirror system 312 or lens 314. Fiberoptictransmission has the added benefit of allowing the laser source 310 tobe positioned remotely from the other system elements, simplifyingsystem design. The speed of the first mirror and/or second mirrors ofthe galvanometer mirror system 312 can be adjusted during part of thescan in order to increase or decrease dwell time over a portion of thescan pattern, thereby adjusting the corresponding dose of UV lightapplied in portions of the scan pattern.

The treatment system 300 also includes an eye tracking system. Inparticular, the treatment system 300 includes an eye position andorientation detecting system 316 (e.g., a camera that captures images ofthe eye 1). The controller 320 can receive and process the information(e.g., images) from the eye position detecting system 316 to determinethe position of the cornea 2 relative to the treatment system 300. Tocompensate for changes in the position of the cornea 2, the controller320 can control the galvanometer mirror system 312 to adjust the scannedlaser beam and cause the scan pattern 10 to be applied to the desiredareas of the cornea 2. As such, the detecting system 316 and thecontroller 320 combine to provide an eye tracking system.

In general, scanning treatment systems can apply photoactivating lightaccording to a pattern to achieve a predefined treatment zone (e.g.,circular, annular, or other shape) at the corneal surface. Aspects of ascan pattern may be defined by a continuous line. As shown with theexample patterns 200 a, 200 b of FIGS. 2A-B, a continuous line mayformed by scanning the laser in connected piecewise paths.

Alternatively, a continuous line may formed by scanning the laserwithout interruption. For instance, as shown in FIGS. 4A-C, a continuousline may formed by scanning the laser in a spiral 404 withoutinterruption.

Additionally or alternatively, aspects of a scan pattern may be definedby a plurality of unconnected straight or curved lines. For instance, ascan pattern may include lines defined by a series of dashes.

Additionally or alternatively, aspects of a scan pattern may be definedby a plurality of discrete dots. For instance, a scan pattern mayinclude lines defined by a series of discrete dots. In some embodiments,a sequence of discrete dots can be applied with an optical element, suchas a diffractive element as described further below, to simultaneouslyform multiple laser spots which are individually scanned to define thetreatment zone.

Various types of patterns of photoactivating light for cross-linkingtreatments are described herein. The choice of pattern may depend ondifferent optimization criteria including, but not limited to,uniformity of photoactivating light dose over the treatment zone,desired maximum cross-linking efficiency, and maximum correction (e.g.,refractive correction) for the eye. Furthermore, the choice of patternmay be constrained by considerations including, but not limited to,compliance to eye safety standards, predefined treatment time,predefined light dose, limits on scan velocity imposed by opticalelements and other components of the treatment system, and laser powerspecifications.

Laser Scanning Optimization

Using a laser light source to achieve a scanned light pattern canprovide benefits for corneal cross-linking treatments over approachesthat employ a LED light source. In particular, scanning parameters forthe laser can be optimized to increase the efficacy of individualtreatments. For instance, treatment time, total dose,intensity/irradiance of the laser beam, pulsing of the laser beam, sizeof the spot defined by the laser beam (laser spot size), velocity orduration of application of the laser spot, and/or frequency ofrepetition of portions of the scan pattern can be controlled to enhancecross-linking activity. Such parameters can be optimized according tothe photochemical kinetic reactions involved in cross-linking activityas described above. These reactions determine the consumption andreplenishment of oxygen during cross-linking activity, supply andphoto-degradation of the cross-linking agent molecules, and depth ofeffect.

For instance, laser spot size can be optimized to achieve the desiredtreatment. FIGS. 4A-C also illustrate how different treatment zones canbe achieved by varying the laser spot size. In particular, FIG. 4Aillustrates an example treatment zone 400 a where a beam from a lasersource, e.g., the UV laser source 210 or the UV light source 310, formsa spot size with a diameter 402 a that is sufficiently large to applyphotoactivating light in a spiral 404 to 100% of an area 408 defined bya substantially circular boundary 406. Meanwhile, FIG. 4B illustrates anexample treatment zone 400 b where a beam from the laser source has aspot size with a diameter 402 b that is 50% of the diameter shown inFIG. 4A. As such, as the beam in FIG. 4B travels over the same spiral404, photoactivating light is applied to less of the area 408 defined bythe substantially circular boundary 406. As shown in FIG. 4B, thediameter 402 b is too small to allow the laser beam to cover the spacebetween adjacent portions of the spiral 404. FIG. 4C illustrates yetanother example treatment zone 400 c where a beam from the laser sourcehas a spot size with a diameter 402 c that is 25% of the diameter 402 ashown in FIG. 4A. As such, as the beam in FIG. 4C travels over the samespiral 404, photoactivating light is applied even less of the area 408defined by the substantially circular boundary 406. Accordingly, varyingthe laser spot size can determine the areas of the cornea (treatmentzone) that receive photoactivating light and experience cross-linkingactivity. Optimizing the size of the laser spot in relation to the pitchof the spiral pattern has the effect of increasing oxygen diffusion intothe treated spots from the untreated spots, which is advantageous formaintaining an aerobic state in the treated spots and thereforeincreasing crosslinking efficiency.

Additionally or alternatively, frequency of repetition for portions ofthe scan pattern can be optimized to achieve the desired treatment. Forinstance, the laser beam may travel over portions of a given scanpattern more than once. Furthermore, the laser beam may be scanned overthese portions in different sequences. For instance, a scan pattern mayinclude portions A, B, and C. In an initial pass, the laser beam maytravel over portion A, then portion B, and then portion C. During asubsequent pass, the laser beam may travel over portion C, then portionB second, and then portion A. The laser beam may also transform aspectsof the scan pattern as it travels over portions of the given scan morethan once. For instance, during a subsequent pass by the laser beam, thescan pattern or portions thereof may be rotated and/or shifted laterallyrelative to the first pass. Optimizing the frequency of repetition ofthe scan pattern has the effect of preventing depletion of oxygen withinthe treated spots, which is advantageous for maintaining an aerobicstate in the treated spots and therefore increasing crosslinkingefficiency.

Additionally or alternatively, characteristics of the laser beamdelivered to the XY scanning system can be optimized to achieve desiredtreatment. For instance, the laser beam may be delivered according toparticular pulsing parameters as described above. In some cases, apulsed laser beam may be delivered to the XY scanning system while theXY scanning system travels continuously over selected portions of thescan pattern, so that a pattern of dashes is generated over thoseportions.

The intensity and/or duration of the laser beam delivered to the XYscanning system at different portions of the scan pattern can beoptimized to provide desired doses of photoactivating light at desiredareas of the treatment zone. For instance, the intensity of the laserbeam may be modulated for selected portions of the scan pattern to applydifferent irradiances at different locations on the cornea. The laserbeam may also be applied with particular durations and irradiance forselected portions of the scan pattern.

If a continuous scan pattern such as spiral pattern is applied, thepitch between spiral lines can additionally be optimized. If adiscontinuous scan pattern such as a random, semi-random, ormatrix-based pattern is applied, the dwell time on each spot, distancebetween spots, and travel time between spots can additionally beoptimized.

FIG. 5 illustrates a flowchart for an example process 500 for optimizinglaser scanning parameters for cross-linking treatments. An initialtreatment time 502 a, a dose 502 b of photoactivating light, a pitch 502c for the scan pattern, and an initial repetition rate 502 d arespecified for the optimization process 500. In act 504, the optimizationprocess 500 calculates a laser power based on the initial treatment time502 a, the initial dose 502 b, and the pitch 502 c. In act 506, theoptimization process 506 determines whether the calculated laser poweraffects the photostability of the cross-linking agent. If photostabilityis affected, the optimization process 500 returns to act 504 torecalculate the laser power until it determines, in act 506, that thephotostability is not affected. In act 510, the optimization process 500selects the laser power which does not affect photostability. In act512, the optimization process 500 recalculates the treatment time basedon the selected laser power. In act 514, the optimization process 500calculates a duty cycle based on the initial repetition rate 502 d andthe selected laser power. In act 516, the optimization process 500compares oxygen depletion and oxygen replenishment with the calculatedduty rate. If oxygen depletion is less than oxygen replenishment, theoptimization process 500 increases the repetition rate in 518 andreturns to act 514 where it recalculates the duty cycle based on theincreased repetition rate. The optimization process 500 selects the dutycycle in act 520 once it determines that the oxygen depletion is notless than oxygen replenishment. In act 522, the optimization process 500calculates an irradiance for the photoactivating light based on theselected duty cycle. The optimization process may conceptually becompleted once or a discrete number of times, for example in alaboratory, in order to generate a preset list of optimized parametercombinations. Alternatively, the optimization process may be conductedon demand by software in response to user inputs in order to generate aspecific parameter combination prior to treatment.

Certain scanning parameters may be related. For instance, if the totaldose is kept constant, increasing the laser power decreases thetreatment time, or vice versa. Experimental data indicates that longertreatment times and higher repetition rates usually result in asignificant increase in flattening of the cornea, while the change inthe laser power does not significantly affect flattening. (It is noted,however, extremely high laser powers, in addition raising safetyconcerns, can adversely affect flattening by degrading drug molecules toby-products that produce less efficient cross-linking.)

Experimental results indicate that increasing repetition rate, thusincreasing the number of visits to the same location by the laser beam,can significantly enhance cross-linking activity. To achieve greaterflattening, the repetition rate, or equivalently the number of visits,can be increased until the time for oxygen replenishment is on the orderof the off-duty duration for each location. This allows sufficient timebetween two consecutive visits for the oxygen to replenish at eachlocation. FIG. 6 illustrates an example repetition cycle 600 for across-linking treatment. During each visit, one location receives aspecific amount of laser irradiance for photoactivation, followed by anoff-cycle where the laser beam is delivered to other locations. Thetotal irradiance per location per repetition depends on the scanvelocity as well as the laser power. The number of laser visits perlocation is maximized while the off-duty duration is sufficient to allowoxygen replenishment. Preferably, the on-duty duration is shorter thanthe time needed for complete oxygen depletion.

FIG. 7 illustrates oxygen concentration and fluorescent intensityindicating the presence of the cross-linking agent at a location duringan example treatment. Laser scanning is optimized based on experimentson ex-vivo porcine eyes. In particular, the dose is 15 J/cm², thetreatment time is 18 min, and the laser power is 1.75 mW. The circulartreatment zone has a 4 mm diameter and the scan pattern covers thetreatment zone fully (full pitch). Oxygen is measured under a 200 μmflap. The fluorescent intensity is measured by averaging 520-540 nmwavelengths. FIG. 7 shows that 8 Hz repetition frequency provides a goodbalance between oxygen depletion and replenishment at each repetitioncycle, so that the oxygen level at the depth of 200 μm is still slightlyabove zero. The drug is consumed during the treatment, and the rate ofdrug destruction by the laser beam is negligible.

Correspondingly, FIGS. 8A-E show the curvature change resulting fromtreatments of five eyes where the epithelium layer is left on the eye(epi-on). Meanwhile, FIGS. 9A-E show the curvature change resulting fromtreatments of five eyes where the epithelium layer is entirely removed(epi-off). The experimental results indicate that laser scanning withthe parameters above and a repetition frequency of 8 Hz provides greaterflattening than treatments than treatments using UV LED.

As described above, the rate of corneal cross-linking activity islimited by oxygen concentrations in the corneal tissue. Thus,embodiments can optimize parameters for laser scanning to achieve scanpatterns that affect depletion/replenishment of oxygen for cross-linkingactivity. In an example implementation, a pulsed laser beam is scannedover corneal tissue with a 50% duty cycle and a fixed pulse frequency.As the laser beam scans a pattern, the laser beam leaves unexposedregions of corneal tissue before and after each exposed region along thescan. The exposed regions receive photoactivating light from the laserbeam, and the resulting cross-linking activity depletes oxygen in theexposed region. Advantageously, the adjacent unexposed regions enhancethe diffusion of oxygen back into an exposed region after the laser beamleaves the exposed region. The pattern scanned by the laser beam can bedithered back and forth to ensure that cross-linking activity isgenerated over the entire desired treatment area. In some cases, thepulse may be selected based on the scan velocity to expose a region ofcorneal tissue approximately equal to the diameter of the laser beam ata time.

FIG. 19A illustrates an example annular treatment pattern 1900 a with anouter diameter of approximately 4 mm. FIG. 19B illustrates an exampleannular treatment pattern 1900 b with an outer diameter of approximately8 mm. The treatment patterns 1900 a, b are produced by pulsing a laserbeam at a 50% duty cycle and a fixed pulse frequency over a spiral scan(spiraling inwardly toward a center). The shaded spots indicate theexposed regions where the laser beam is “on” and the unshaded spotsindicate the adjacent unexposed regions where the laser beam is “off.”The size of the exposed regions is determined by pulse frequency andscan velocity.

To produce the patterns 1900 a, b, the formulas relating to scanparameters may be given by the following:

-   -   Input:        -   D_(min)—inner diameter of annular treatment pattern        -   D_(max)—outer diameter of annular treatment pattern        -   P_(r)—pitch in radial direction        -   f_(upd)—update frequency        -   θ₀—initial spiral angle (changing θ₀ rotates the spiral)    -   Formulas:        -   spiral update time:

$\begin{matrix}{t_{upd} = \frac{1}{f_{upd}}} & (1)\end{matrix}$

-   -   -   spiral length:

$\begin{matrix}{L_{sp} = \frac{\pi \cdot \left( {D_{\max}^{2} - D_{\min}^{2}} \right)}{4 \cdot P_{r}}} & (2)\end{matrix}$

-   -   -   linear velocity:

V=f _(upd) ·L _(sp)  (3)

-   -   -   time constant (for spiral formula below):

$\begin{matrix}{\tau = \frac{t_{upd}}{1 - \left( \frac{D_{\min}}{D_{\max}} \right)^{2}}} & (4)\end{matrix}$

-   -   -   spiral angle (for spiral formula below):

$\begin{matrix}{\theta_{sp} = \sqrt{V \cdot \frac{4{\pi\tau}}{P_{r}}}} & (5)\end{matrix}$

-   -   -   number of loops:

N _(Lps)=(D _(max) −D _(min))/(2·P _(r))  (6)

-   -   -   spiral formula (t∈[0, t_(upd)]):

$\begin{matrix}{{\theta(t)} = {\theta_{0} + \theta_{sp} - \sqrt{V \cdot \frac{4{\pi\left( {\tau - t} \right)}}{P_{r}}}}} & (7)\end{matrix}$ $\begin{matrix}{{r(t)} = \sqrt{{V \cdot P_{r} \cdot \left( {\tau - t} \right)}/\pi}} & (8)\end{matrix}$ $\begin{matrix}{{r(t)} = {\frac{P_{r}}{2\pi} \cdot \left( {\theta_{0} + \theta_{sp} - {\theta(t)}} \right)}} & (9)\end{matrix}$ $\begin{matrix}{{\theta(0)} = \theta_{0}} & (10)\end{matrix}$ $\begin{matrix}{{r(0)} = {D_{\max}/2}} & (11)\end{matrix}$ $\begin{matrix}{{t\left( t_{upd} \right)} = {D_{\min}/2}} & (12)\end{matrix}$

-   -   -   wave formula:

x(t)=r(t)·cos(θ(t))  (13)

y(t)=r(t)·sin(θ(t))  (14)

In another example implementation, a pulsed laser beam may be scannedover corneal tissue with a 50% duty cycle and a variable pulse frequencyso that the laser beam leaves unexposed regions of corneal tissue on allfour sides of each exposed region in the resulting pattern. Theresulting pattern resembles a checkerboard. Advantageously, compared tothe laser beam with fixed pulsed frequency described above, the adjacentunexposed regions of corneal tissue on all four sides of an exposedregion promotes greater diffusion of oxygen back into the exposed regionafter the laser beam leaves the exposed region. The pulse frequency canbe varied between predefined minimum and maximum values, resulting incorresponding minimum and maximum exposure regions.

FIG. 20A illustrates an example annular treatment pattern 2000 a with anouter diameter of approximately 4 mm. FIG. 20B illustrates an exampleannular treatment pattern 2000 b with an outer diameter of approximately8 mm. The treatment patterns 2000 a, b are produced by pulsing a laserbeam at a 50% duty cycle and a variable pulse frequency over a spiralpattern (spiraling inwardly toward the center). The shaded regions inFIGS. 20A-B indicate the exposed regions where the laser beam is “on”and the unshaded regions indicate the adjacent unexposed regions wherethe laser beam is “off.”

To produce the patterns 2000 a, b, the formulas relating to scanparameters may be given by the following:

-   -   Input:        -   DC—duty cycle        -   N_(sct)—number of sectors over 2π rad angle    -   Formulas:        -   angular pitch:

Δθ=2π/N _(sct)  (15)

-   -   -   number of spots:

$\begin{matrix}{N_{spt} = {{{round}\left( \frac{{\theta\left( \tau_{upd} \right)} - \theta_{0}}{\Delta\theta} \right)} + 1}} & (16)\end{matrix}$

-   -   -   sot counter:

nsp=1,2, . . . ,N _(spt)  (17)

-   -   -   meridional angles:

θm _(nsp)=θ₀+(nsp−1)·Δθ  (18)

-   -   -   loop numbers (may be fractional):

$\begin{matrix}{{nLp}_{nsp} = \frac{\left( {{nsp} - 1} \right) \cdot {\Delta\theta}}{2\pi}} & (19)\end{matrix}$

-   -   -   even/odd loop index (in the range from −1 to 1):

ii _(nsp)=rem(nLp _(nsp),2)−1  (20)

-   -   -   laser on angle:

θon_(nsp) =θmn _(sp) +ii _(nsp)·Δθ/2  (21)

-   -   -   laser off angle:

θoff_(nsp)=θon_(nsp)+Δθ·DC  (22)

-   -   -   laser on time:

$\begin{matrix}{{ton}_{nsp} = {\tau - {\frac{P_{r}}{4{\pi \cdot V}} \cdot \left( {\theta_{0} + \theta_{sp} - {\theta on}_{nsp}} \right)^{2}}}} & (23)\end{matrix}$

-   -   -   laser off time:

$\begin{matrix}{{toff}_{nsp} = {\tau - {\frac{P_{r}}{4{\pi \cdot V}} \cdot \left( {\theta_{0} + \theta_{sp} - {\theta off}_{nsp}} \right)^{2}}}} & (24)\end{matrix}$

-   -   -   instantaneous laser modulation frequency:

$\begin{matrix}{{f_{Las}(t)} = \frac{V}{{\Delta\theta} \cdot {r(t)}}} & (25)\end{matrix}$

Implementations of the laser beam with variable pulse frequency mayemploy a laser modulation signal that sets laser on/off times tocoincide with a predefined number of meridians in the treatment pattern.

The size of the exposed regions is determined by pulse frequency andscan velocity, but the pulse frequency may vary in relation to theradial position of the laser beam. In particular, the modulation signalmay have a variable frequency that increases toward the center of thespiral. The instantaneous laser modulation frequency is given byequation (25), where the linear velocity is given by equation (3). Theradial pitch of the laser modulation is not constant.

When implementing the laser beam with variable pulse frequency, theexposed regions may become smaller and smaller as the laser beamapproaches the center of the treatment pattern. FIG. 20C illustrates anexample annular treatment pattern 2000 c with an outer diameter ofapproximately 9 mm, produced by a laser beam with variable pulsefrequency. The shaded regions in FIG. 20C indicate the exposed regionswhere the laser beam is “on” and the unshaded regions indicate theunexposed regions where the laser beam is “off.” As shown particularlyin FIG. 20C, a tiered set of meridians may be employed to keep theexposed regions within a predefined range of sizes.

The laser modulation signal is synchronized with the drive signal forthe galvanometer—the laser modulation signal can reset and alternate ateach spiral restart. FIG. 21 illustrates example waveforms 2100 a(Galvo-x, Galvo-y) for driving a galvanometer as well as a lasermodulation waveform 2100 b during a portion of a cross-linkingtreatment. As shown in FIG. 21 , the laser modulation frequency varieswith time and becomes greater as the laser beam spirals inwardly towardthe center of the pattern. Meanwhile, the instantaneous laser duty cycleremains at a constant 50%.

FIG. 22A illustrates example waveforms 2200 a (Galvo-x, Galvo-y) fordriving a galvanometer during a complete cross-linking treatment.Correspondingly, FIG. 22B illustrates a laser modulation waveform 2200 bduring the complete treatment. The laser modulation frequency increasesrapidly near the end of the scan when the laser beam is near the centerof the treatment pattern. This may cause the exposed tissue area tobecome too small near the center and can also increase the complexity ofthe electronic circuitry needed to drive the laser.

To overcome the potential problem of undesirably high laser modulationfrequencies near the center of the treatment pattern, the checkerboardangular pattern can be split into multiple radial zones based on theinstantaneous laser modulation frequency. FIG. 23 illustrates an examplelaser modulation waveform 2300 implementing such an approach. In theoutermost zone, the sector angle has a predefined value and the lasermodulation frequency increases as the laser moves inwardly. As soon asthe modulation frequency reaches a predefined limit, the sector angledoubles and the modulation frequency halves at the onset of the secondzone. Subsequent zones are introduced in the same way. The number ofzones is determined automatically to keep the modulation frequency belowthe predefined limit. (Thus, this approach may be referred herein as an“auto zone” approach.) Initial number of sectors (in the first zone) isa power of two, and the number of sectors halves when switching to thenext zone.

TABLE 1 illustrates example output data for an annular pattern producedby (i) a pulsed laser beam scanned with fixed laser modulationfrequency, (ii) a pulsed laser beam scanned with variable lasermodulation frequency not implementing the auto zone approach, and (iii)a pulsed laser beam scanned with variable laser modulation frequencyemploying the auto zone approach.

TABLE 1 Variable Laser Variable Fixed Frequency Laser Laser (not autoFrequency Parameter Frequency zone) (auto zone) Number of zones 1 1 6Number of spots 6361 1114 3993 Spiral length, mm 636.1 636.1 636.1 Scanvelocity, m/s 10.2 10.2 10.2 Minimum spot scan length, μm 50 6.0 μm 50.7Maximum spot scan length, μm 50 565.6 110.5 Minimum laser modulation101.8 9.0 46.1 frequency, kHz Maximum laser modulation 101.8 809.9 100.2frequency, kHz Minimum pulse width, μs 4.9 0.62 5

The common input parameters for the patterns in TABLE 1 include:

-   -   inner diameter of pattern: 100 μm    -   outer diameter of patter: 9 mm    -   laser beam (spot) diameter: 100 μm    -   radial pitch: 100 μm    -   update frequency: 16 Hz    -   duty cycle: 50%

For the pulsed laser beam scanned with fixed laser modulation frequency,the input further includes a tangential pitch equal to 100 μm. For thepulsed laser beam scanned with variable laser modulation frequency notimplementing the auto zone approach, the input further includes a numberof sectors equal to 25. For the pulsed laser beam scanned with variablelaser modulation frequency implementing the auto zone approach, theinput further includes an initial number of sectors equal to 128 and amodulation frequency limit equal to 100 kHz.

FIG. 24A illustrates an example annular treatment pattern 2400 a with anouter diameter of approximately 4 mm, produced with a pulsed laser beamscanned with variable laser modulation frequency implementing the autozone approach (i.e., laser modulation waveform split into multipleradial zones based on a modulation frequency limit). FIG. 24Billustrates an example laser modulation waveform 2400 b corresponding tothe treatment pattern 2400 a.

The input parameters for the pattern 2400 a include:

-   -   inner diameter of pattern: 85 μm    -   outer diameter of pattern: 4 mm    -   radial pitch: 85 μm    -   update frequency: 16 Hz    -   maximum number of meridians: 64    -   maximum modulation frequency: 22 kHz

The output data for the pattern 2400 a include:

-   -   number of zones: 6    -   spiral length: 147.8 mm    -   scan velocity: 2.3644 m/s    -   minimum modulation length: 52.4 μm    -   maximum modulation length: 107.2 μm    -   minimum laser modulation frequency: 11.014 kHz    -   maximum laser modulation frequency: 22.139 kHz

FIG. 25A illustrates an example annular treatment pattern 2500 a with anouter diameter of approximately 9 mm, produced with a pulsed laser beamscanned with variable laser modulation frequency implementing the autozone approach. FIG. 25B illustrates an example laser modulation waveform2500 b corresponding to the treatment pattern 2500 a.

The input parameters for the pattern 2500 a include:

-   -   inner diameter of pattern: 85 μm    -   outer diameter of pattern: 9 mm    -   radial pitch: 85 μm    -   update frequency: 16 Hz    -   maximum number of meridians: 128    -   maximum modulation frequency: 75 kHz

The output data for the pattern 2500 a include:

-   -   number of zones: 7    -   spiral length: 748.37 mm    -   scan velocity: 11.9739 m/s    -   minimum modulation length: 74.37 μm    -   maximum modulation length: 159.60 μm    -   minimum laser modulation frequency: 37.507 kHz    -   maximum laser modulation frequency: 76.225 kHz

FIG. 26A illustrates an example annular treatment pattern 2600 a with anouter diameter of approximately 9 mm, produced with a pulsed laser beamscanned with variable laser modulation frequency implementing the autozone approach. FIG. 26B illustrates an example laser modulation waveform2600 b corresponding to the treatment pattern 2600 a.

The input parameters for the pattern 2600 a include:

-   -   inner diameter of pattern: 5 mm    -   outer diameter of pattern: 9 mm    -   radial pitch: 85 μm    -   update frequency: 16 Hz    -   maximum number of meridians: 128    -   maximum modulation frequency: 75 kHz

The output data for the pattern 2600 a include:

-   -   number of zones: 1    -   spiral length: 517.4 mm    -   scan velocity: 8.279 m/s    -   minimum modulation length: 61.34 μm    -   maximum modulation length: 110.45 μm    -   minimum laser modulation frequency: 37.47 kHz    -   maximum laser modulation frequency: 67.47 kHz        Although the auto zone approach is employed, the pattern        includes only one zone.

FIG. 27 illustrates aspects of a spot profile 2700 produced by a pulsedlaser beam traveling along a scan s. As shown in FIG. 27 , the laserbeam has a laser spot diameter D_(sp) and produces a scan length L_(SC)which is a product of the scan velocity V_(SC) and pulse width t_(p).

The following parameters may be employed to produce a pattern with anouter diameter of 9 mm, for instance:

-   -   scan velocity V_(SC): 10.2 m/s    -   laser spot diameter D_(sp): 100 μm    -   radial pitch: 100 μm    -   duty cycle: 50%    -   spot profile: flattop and Gaussian    -   laser power: 8 mW

The modulation frequency can be optimized. In the case of a Gaussianlaser beam, the modulation frequency is preferably less than 50 kHz tomaintain sufficient contrast in dose between treated and untreated spotsin a single scan. For instance, at 50 kHz, the contrast ((max−min)/mean)is approximately 50%. This estimate depends on spot profile (inner andouter diameters) and galvanometer velocity. FIGS. 28A-D illustratecontrast as a function of modulation frequency. FIG. 28A illustrates aGaussian laser spot with a laser modulation frequency of 25 kHz. FIG.28B illustrates a Gaussian laser spot with a laser modulation frequencyof 50 kHz. FIG. 28C illustrates a Gaussian laser spot with a lasermodulation frequency of 75 kHz. FIG. 28D illustrates a Gaussian laserspot with a modulation frequency of 100 kHz.

TABLE 2A provides input parameters for producing various annulartreatment patterns A-F via pulsed laser scanning implementing the autozone approach. Correspondingly, TABLE 2B provides output data for thevarious treatment patterns A-F. The requirement imposed onto thepatterns A-F is a minimum modulation length of 85 μm.

TABLE 2A Input Parameters A B C D E F Outer diameter, 4 8 8 9 9 9 mmInner diameter, mm 0.085 4 3 4 85 85 Repetition 16 16 16 16 8 16Frequency, Hz Pitch, μm 85 85 85 85 85 85 Maximum # of 64 128 128 128128 128 Meridians Maximum 13.75 41 47 48 35 70 Modulation Frequency, kHz

TABLE 2B Output Data A B C D E F Number of zones 6 2 3 2 7 7 Spirallength, mm 147.8 443.519 508.20 517.44 748.37 748.37 Scan velocity, m/s2.3644 7.0963 8.1312 8.279 5.987 11.9739 Minimum 85.0 86.5 86.5 86.285.3 85.3 modulation length, μm Maximum 171.6 173.00 172.91 172.4 171.0171.0 modulation length, μm Minimum laser 6.88 20.51 23.51 24.01 17.5035.00 modulation frequency, kHz Maximum laser 13.77 41.00 47.01 48.0135.00 70.00 modulation frequency, kHz Minimum pulse 35.9714 12.193510.6356 10.414 14.2501 7.1251 width, μs

Point and Shoot Laser Scanning Approach

As described above, aspects of a scan pattern may be defined by aplurality of discrete dots. A treatment pattern may be defined byscanning discrete dots in randomized manner or a semi-randomized mannerbased on continuous x, y variables.

According to some embodiments, a point and shoot technique may beemployed to apply a sequence of discrete dots and achieve a desiredtreatment zone. As shown in FIG. 10 , a scan pattern 1000 may be definedby scanning discrete dots 1002 according to a grid 1006 inside aboundary 1004 (e.g., a circular boundary) defining the treatment zone.In particular, the grid 1006 includes an arrangement of hexagonal cells1007, where the dots 1002 are sampled (shot) into the hexagonal cells1007 by the laser beam. The hexagonal cells 1007 may be arranged tospace the dots 1002 uniformly within the boundary 1004, i.e., tomaximize homogeneity of the photoactivating light across the treatmentzone. The size (e.g., diameter) of the laser beam spot and the pitch ofthe grid 1006 may be matched to maximize this homogeneity.

After the grid of the scan pattern has been defined, the order forshooting the laser beam spots into the cells of the grid can beoptimized. The order of shots, duration of shots, intensity of shots,and the number of repeated shots into each cell may affect theefficiency of cross-linking activity and the desired amount of cornealshape change. According to one approach, each cell is sampled at leastonce in a random order. According to another approach, the treatmentsystem tracks the total dose delivered to each cell based on theaccumulation of shots received. In other words, the treatment systemmaintains a dose map as treatment progresses and determines where todeliver the next shot according to this dose map. During the treatment,the treatment system may deliver the next shot to the cell with thelowest total dose (which may be the cell that has received the fewestnumber of shots). If more than one cell has the lowest total dose, thetreatment system may also select, for the next shot, a cell that islocated the greatest distance from the cell receiving the previous shot.Selecting cells based on greatest distance between consecutive shots mayprovide more efficient and uniform cross-linking activity across thescan pattern. In particular, greater distance between shots may improvethe local supply of oxygen for cross-linking at the next cell.Additionally, the effect of activity at the previous cell (cross-talk)is less likely to affect the activity at a next cell that is a greaterdistance away from the previous cell.

A possible downside of selecting cells to maximize distance betweenconsecutive shots is the increased time between the applications of theconsecutive shots due to the time to move across the distance (transittime). Accordingly, to address this possible downside, the treatmentsystem may constrain the distance between consecutive shots, e.g., thedistance is maximized but does not exceed a predefined maximum traveldistance (MTD). Thus, the treatment system may choose a cell with theminimum total dose within the MTD. Where all cells have received thesame dose or the same number of shots, the treatment system may selectthe next cell randomly.

In general, the point and shoot technique can be optimized according tovarious parameters to achieve the desired treatment. Such parametersinclude, but are not limited to: (i) size of the laser beam spot; (ii)pitch of the grid; (iii) number of shots per cell across the scanpattern (also known as visits); (iv) total treatment time; (v)irradiance of the laser beam; (vi) amount of time between application ofconsecutive dots; and/or (vi) the order in which the spots are applied.For instance, FIG. 11 illustrates different combinations of parametervalues for treatments employing a hexagonal grid within a circularboundary (corresponding to the treatment zone) with a diameter ofapproximately 4 mm where the dose is 15 J/cm² UVA light, the treatmenttime is approximately 1000 seconds, the time required to transit betweenconsecutive spots is approximately 0.2 milliseconds, and the spotprofile is Gaussian. The parameters in FIG. 11 include a size of thelaser beam spot measured as a diameter D_(sp) (μm) full width at halfmaximum (FWHM), a pitch of the grid (μm), number of visits (where avisit corresponds to a single pass of the scan pattern resulting in allcells receiving a shot), the number of spots across the scan pattern,the number of shots, the time for each visit (s), time for each shot(ms) (shooting time), peak irradiance (W/cm²), power of the laser beam(mW), peak dose per shot (J/cm²), and nonuniformity (%).

FIGS. 12A-C illustrate graphs for implementations of the treatmentparameters shown in row B of FIG. 11 using a galvanometer mirror system(e.g., the galvanometer mirror system 312 shown in FIG. 3 ). Each graphshows the drive voltage applied to induce a tilt angle of the X mirroras a function of time as the treatment progresses. In particular, themirror tilt angle is expressed in terms of the X voltage that controlsthe X mirror as described above. The mirror tilt angle remains fixedwhen a shot is delivered to a cell (during the shooting time) and variesas the galvanometer mirror system is adjusted to deliver a shot to thenext cell (during the transit time). No photoactivating light isdelivered to the galvanometer mirror system during the transit time.Practically, when the galvanometer mirror system is adjusted to delivera shot to the next cell, a transient time is needed to allow the mirrorsto stop moving. According to one approach, the laser beam is modulatedand the galvanometer mirror system is synchronized so thatphotoactivating light is not delivered to the galvanometer mirror systemduring this transient time. FIG. 12A shows the tilt angle (X voltage)during the first ten shots of a treatment where travel distance isunconstrained, i.e., MTD=∞. FIG. 12B shows the tilt angle (X voltage)during the first ten shots of a treatment where travel distance isconstrained to a travel distance of no greater than ten times thediameter D_(sp) (100 μM), i.e., MTD=10 D_(sp). FIG. 12C shows the tiltangle (X voltage) during the first ten shots of a treatment where traveldistance is further constrained to a travel distance of no greater thanfive times the diameter D_(sp) (100 μm), i.e., MTD=5 D_(sp). FIGS. 12A-Cdemonstrate that constraining the travel distance to a few multiples ofthe laser spot size results in shorter travel distances betweenconsecutive spots, i.e., smaller changes in tilt angle between spots.

Eye Motion Correction

As described above, the treatment system 300 shown in FIG. 3 includes aneye tracking system to account for motion of the eye 1 during treatment.According to some approaches, the position of the eye is monitoredduring treatment by processing images captured by an imaging system. Inresponse, the treatment system dynamically adjusts the delivery ofphotoactivating light so that the pattern is applied to desired areas ofthe cornea.

As shown in the timeline 1300 of FIG. 13 , however, there is a delaybetween detection of the eye position and delivery of thephotoactivating light due to discrete-time detection of the eye andfinite response time of the treatment system. For instance, FIG. 13shows that the imaging system captures an image i of the eye. The imagei is processed and a position of the eye in image i is calculated to beX(i). The position X(i) is then processed to calculate the position ofthe desired treatment zone and photoactivating light H(i) is deliveredto the desired treatment zone. The time required to process the image iresults in a system delay of 61. Additionally, the time required toprocess the position X(i) and trigger delivery of the photoactivatinglight results in another system delay of 62. Thus, the total time A fromthe time that image i is captured to the time that photoactivating lightis actually delivered is at least the sum of system delays 61 and 62.Accordingly, inaccuracies in the delivery of the photoactivating lightmay result if there is further eye movement during the delay time A.

Rapid eye movements, in particular, can cause location error in thedelivery of the photoactivating light due to this delay. With the pointand shoot approach above, the location error can be significant if thelaser spot size is comparable to the amount of eye movement during thedelay time. FIGS. 14(A)-(D) illustrate a grid 1406 defined by anarrangement of hexagonal cells 1407 for a grid-based point and shootapproach. As shown in FIG. 14(A), the treatment system intends todeliver a shot to a cell 1407 a at time (i−Δ). An imaging systemcaptures a series of frames from which the position of the eye and therelative location of the shot can be determined. In particular, FIGS.14(B) and 14(C) illustrate consecutive frames at times i and (i+1),respectively. The frames show that the eye has moved and that the shothas been received by other unintended cells (location error). The grid1406 is fixed relative to the eye and thus the location of the shot hasmoved relative to the grid 1406. As shown in FIG. 14(B), the shot isreceived across parts of cells 1407 a-d at time i. Meanwhile, FIG. 14(C)shows that the shot is received across parts of cells 1407 a, d, e attime (i+1).

A motion model (e.g., linear model, Kalman filter, or FIR filter) isemployed to model eye motion between consecutive frames and to determinethe cells that receive photoactivating light between consecutive frames.The dose map can then be updated to indicate that each of such cells hasreceived a dose of photoactivating light proportional to the areacovered by the photoactivating light in the frames. Thus, as shown inFIG. 14(D), the dose map indicates that a dose of photoactivating lighthas been received by the cells 1407 a-e based on the information in theframes at times i and (i+1). Moreover, as shown with the relativeshading of the cells 1407 a-e in FIG. 14(D), the dose map indicates therelative doses of photoactivating light that the cells 1407 a-e havereceived. For instance, based on the total area of each cell 1407 a-ecovered by the photoactivating light in both frames, the cell 1407 a hasreceived the greatest dose, while the cells 1407 c, d have receivedgreater doses than the cells 1407 b, e. The updated dose map can then beused to determine the location of the next shot as described above.Accordingly, FIG. 14 illustrates a modification of the grid-based pointand shoot approach that employs the dose map to account for the effectsof location error.

Although FIG. 14 illustrates modification of the grid-based point andshoot approach, other approaches for scanning photoactivating lightacross a cornea may include a similar mechanism whereby a dose map isdynamically updated to account for measured errors in delivery ofphotoactivating light and the scanning path is dynamically adjusted tospatially optimize applied doses during the treatment. Furthermore, inalternative embodiments, fluorescent signals resulting from theapplication of photoactivating light may be detected to determine thelocation of such application and account for eye motion as describedabove.

Lissajou Curve Scanning

Referring to the treatment system 300 of FIG. 3 , the galvanometermirror system 312 can be employed to create Lissajou curve scanpatterns. Such scan patterns can be translated into independent mirrordrive waveforms that cause the X mirror 312 a and the Y mirror 312 b toscan the laser beam in the x- and y-directions, respectively. Forinstance, each of the mirrors 312 a, b can perform respective sine wavemovements which can be described as:

x=X sin(ω_(x) t+δ)  (26)

y=Y sin(ω_(y) t)  (27)

-   -   where X and Y correspond to the maximum laser beam movement on        the eye surface.        As a specific example, when X=Y=A, ω_(x)=ω_(y)=ω, and δ=90°, the        Lissajou curve is a circle. The beam position and the scanning        velocity at any moment can be described as

s=x+jy=A cos ωt+jA sin ωt=Aej ^(ωt)  (28)=

{dot over (s)}=jωAe ^(jωt)  (29)

In order to cover the entire scanning area, multiple scanning paths areinvolved. The amplitude A is a variable to fit the entire scanning area.In the case of uniform scanning speed:

ωA=constant  (30)

Very dense Lissajou scanning paths may be employed to achieve propercross-linking effect. The process of cross-linking in a region ofcorneal tissue requires a local supply of oxygen as well ascross-linking agent, e.g., riboflavin. As such, the cross-linkingefficiency might decrease if consecutive scanning paths are too close toeach other. To minimize a decrease in cross-linking efficiency, ascanning of n total paths can be interlaced by scanning the n total scanpaths in a sequence defined by an interval m. For instance, if the scanpattern includes n=20 total scan paths (e.g., circular paths) and aninterval m=5 is selected, the scan sequence can start with scan path 1and proceeds to scan paths at every fifth interval after scan path 1,i.e., scan paths 6, 11, 16. The sequence can then move to scan path 2and proceed to scan paths at every fifth interval after scan path 2,i.e., scan paths 7, 12, 17, and so on. The order for the total sequenceis then scan paths 1, 6, 11, 16, 2, 7, 12, 17, 3, 8, 13, 18, 4, 9, 14,19, 5, 10, 15, 20. Alternatively, a sequence can start with scan path 20and proceed in reverse to scan paths at every fifth interval, i.e., theorder for the total sequence is scan paths 20, 15, 10, 5, 19, 14, 9, 4,18, 13, 8, 3, 17, 12, 7, 2, 16, 11, 6, 1.

The scanning of each path can start at any portion of the path. Forinstance, if circular paths are scanned according to the previoussequence, scanning of paths 20, 15, 10, 5 can start at 45° on thecircles; scanning of paths 19, 14, 9, 4 can start from at 40° on thecircles; scanning of paths 18, 13, 8, 3 can start at 35° on the circles;and so on. Because the scan pattern for the entire treatment may involvea large number of scan paths, many start angles may be employed toachieve a uniform distribution of start angles.

Dead Zone Dwelling

In some cases, very high linear scanning speed might be employed foreffective cross-linking. For instance, if linear scanning speed is 3.14mm/ms, a 0.1 mm diameter scanning circle is completed in 0.1 ms and thegalvanometer function frequency ω is 10 kHz. This function frequency isvery difficult to achieve with most commercially available galvanometermirror systems. Indeed, it is common practice to apply one or more notchfilters on a galvanometer servo board to avoid issues associated withresonance in that range. As such, there is a scanning dead zone due tothe limitations of conventional galvanometer performance. Moreover, thisdead zone may create issues for achieving peak power for thephotoactivating light for cross-linking treatment.

The laser beam, however, can move into the dead zone and stay (dwell) inthe dead zone for a short period of time when, for each scan path, thelaser beam scans the portion closest to the dead zone. For instance, ifa cross-linking treatment lasts for a total of 1000 seconds and scansinterlaced paths (e.g., circular scan paths) ten times for each scanpattern at 10 Hz repetition frequency, there are 100,000 opportunitiesto move into the dead zone. If the dead zone size is one percent of thetotal scanning area, the total dwelling time may be 10 seconds, and 100μs for each move into the dead zone (dwelling).

Uniform dead zone dwelling positions can be generated with deterministicequations, but dead zone dwelling can also be achieved randomly. Forinstance, with two 0 to 1 uniformly distributed numbers r₁ and r₂, anddead zone radius is R, random dead zone dwelling position may be:

x=R√{square root over (r ₁)}cos(2πr ₂)  (31)

y=R√{square root over (r ₁)}cos(2πr ₂)  (32)

Laser Power Control and Synchronization

Laser power is synchronized with laser beam position duringcross-linking treatments. Additionally, synchronizing a laser modulationsignal with a position sensor may be employed to maintain precisecontrol over the temporal and spatial characteristics of the scanpattern.

Such synchronization may be necessary because a scan pattern, e.g., withLissajous scan paths, may not correspond exactly with the desiredtreatment area. For instance, the scan pattern may be defined by acircular boundary and circular scan paths, but the zone forcross-linking treatment may not be correspondingly circular. As such, itmay be necessary to turn the laser power on when the laser beam isinside the treatment zone and to turn the laser power off when the laserbeam is outside the treatment zone. Such synchronization may also benecessary because non-uniform laser power is needed for portions of thetreatment zone.

Modulated CW laser output power can be manipulated via triggeringsignals from an acousto-optic modulator or an electro-optic modulator,manipulated directly via diode current, etc. A time delay, also known asrise and fall time, generally occurs when the laser is turned on or off.High quality synchronization accounts for this time delay viacalibration.

The triggering signals for modulation of laser output power can beprovided via an open or closed loop control system. A closed loopcontrol system employs a feedback signal for position. An open loopcontrol system involves careful pre-calibration of time delay associatedwith the triggering signal.

TTL (Transistor-Transistor Logic) generally involves a short rise andfall time and may be employed for digital modulation. Other differentialsignaling such as PECL (Positive Emitter coupled Logic), LV-PECL(Low-Voltage Positive Emitter coupled Logic), and LVDS (Low-VoltageDifferential Signaling) are also able to modulate at high frequencieswith minimal noise.

Stochastic Model, Estimation, and Control for Eye Tracking

Kalman Filter

An algorithm based on the Kalman filter may be employed to remove errorsfrom eye tracking measurements. The Kalman filter is a set ofmathematical equations that implement a predictor-corrector type ofestimator for a stochastic system. It is optimal in the sense ofminimizing the estimated error when some presumed conditions are met.With the Kalman filter, eye tracking accuracy can be significantlyimproved, in contrast to approaches that use direct measurements of eyeposition. Such eye tracking can effectively estimate eye movement with aregular position-velocity-acceleration component and occasional randomcomponent. To implement such eye tracking in a two-dimensional space,two independent filters are employed, i.e., one filter for each spatialdimension.

State-Space Model for Kalman Filter

The Kalman filter addresses the general problem of estimating the statex∈

of a discrete-time controlled process that is governed by the linearstochastic difference equation:

x _(k) =Ax _(k-1) +Bu _(k) +w _(k-1)  (33)

With the measurement z∈

,

z _(k) =Hx _(k) +v _(k)  (34)

The random variables w_(k) and v_(k) represent the process andmeasurement noise. They are assumed to be independent, with normalprobability distribution:

p(w)˜N(0,Q)  (35)

p(v)˜N(0,R)  (36)

One defines {circumflex over (x)} _(k) ∈

to be a priori state estimate at step k given knowledge of the processprior to step k, and {circumflex over (x)}_(k)∈

to be a posteriori state estimate at step k given measurement z_(k). Onecan then define a priori and a posteriori estimate errors as e _(k)≡x_(k)−{circumflex over (x)} _(k) and e_(k)≡x_(k)−{circumflex over(x)}_(k). The priori and posteriori estimate error covariances are:

P _(k) =E[e _(k) e _(k) ^(T)]  (37)

P _(k) =E[e _(k) e _(k) ^(T)]  (38)

Discrete Kalman Filter Algorithm

The equations of Kalman filter fall into two groups: time updateequations and measurement update equations:

$\begin{matrix}{{Initial}{estimates}{for}{}{\hat{x}}_{k - 1}{and}{}P_{k - 1}} \\ \downarrow \\{{Time}{update}} \\\left. \downarrow\uparrow \right. \\{{Measurement}{update}}\end{matrix}$

The time update equations are responsible for projecting forward thecurrent state and error covariance estimates to obtain a prioriestimates of the next time step:

Project the state ahead: {circumflex over (x)} _(k) =A{circumflex over(x)} _(k-1) +Bu _(k)  (39)

Project the error covariance: P _(k) =AP _(k-1) A ^(T) +Q  (40)

The measurement update equations are responsible for the feedback. Theyincorporate a new measurement into the a priori estimate to obtain animproved a posteriori estimate.

Compute the Kalman gain: K _(k) =P _(k) H ^(T)(HP _(k) H ^(T)+R)⁻¹  (41)

Update estimate with measurement: {circumflex over (x)} _(k)={circumflex over (x)} _(k) +K _(k)(z _(k) −H{circumflex over (x)} _(k))  (42)

Update the error covariance: P _(k)=(I−K _(k) H)P _(k)   (43)

Raster Scan with Polygon Scanner

FIG. 15 illustrates an example raster scan pattern 1500. In rasterscanning, a laser beam, starting at the top line, sweeps horizontallyleft-to-right at a steady speed, then rapidly moves back to the left,where it can sweep out the next line. Meanwhile, the vertical positionof the laser beam moves steadily downward. The movement can be eithercontinuous or intermittent. When the scan path is complete, the laserbeam can start from the top line or start from a position between thefirst line and second line to do an interlaced scan. With rasterscanning, laser modulation is synchronized with the cross-linkingtreatment area, as described above.

A polygon scan can typically run faster because there is no dead zone aswith a Lassajou curve scan. The vertical movement of a raster scan ismuch slower, and it can be implemented with simple, slow scanning, e.g.,MEMS-based scanning.

Zig-Zag Scan with Resonant Scanner

FIG. 16 illustrates an example zig-zag scan pattern 1600. Similar toraster scan, zig-zag scanning as shown in FIG. 16 involves fasterhorizontal scanning and slower vertical scanning. Zig-zag scanning cansweep horizontally in both directions. The vertical movement can beeither continuous or intermittent. Zig-zag scanning can be implementedwith a resonant scanner. With zig-zag scanning, laser modulation issynchronized with the cross-linking treatment area, as described above.

Alternative Laser Treatment Systems

As described above, using a laser light source to deliver aphotoactivating light pattern can provide benefits for cornealcross-linking treatments over approaches that employ a LED light source.LED light sources may provide light beams of lower optical quality,including low coherence, poor collimation, and/or large diameters. Withlight beams of such low quality, the choice of available patterns forthe delivery of photoactivating light may be more limited and mayrequire more complex and expansive aspherical optics for patternformation.

In addition to the laser-based approaches employing XY scanners asdescribed above, FIGS. 17 and 18 illustrate examples of other treatmentsystems that provide other laser-based approaches for projectingpatterns of photoactivating light to a cornea. In particular, FIG. 17illustrates an example treatment system 1700 that employs a diffractivemulti-beam splitter, and FIG. 18 illustrates an example treatment system1800 that employs a diffractive beam shaper. These treatment systems maybe more efficient for the use of single-mode lasers.

The treatment system 1700 shown in FIG. 17 includes a UV (e.g., UVA)laser source 1710, a beam expander 1711, a two-dimensional beam splitter1712, a laser beam deflector 1713, and a focusing lens 1714. The lasersource 1710 may be implemented with a light amplitude modulator (eitherinternal or external to the laser source 1710). The laser beam from thelaser source 1710 is directed to the beam expander 1711 and theresulting expanded beam is directed to the two-dimensional beam splitter1712 (e.g., a diffractive beam splitter), which generates more than onelaser beam spot. The laser beam deflector 1713 receives and directs thelaser beam spots to the focusing lens 1714, which projects a pattern ofthe laser beam spots to the cornea 2. The spot pattern is generated fromthe laser beam spots at the surface of the cornea 2 with a pattern sizethat is determined by the distance from the cornea 2 to the focusinglens 1714. The cross-linking activity occurs simultaneously at all spotsusing either continuous and/or pulsing laser light.

The treatment system 1700 includes a controller 1720 that may controlaspects of the treatment system 1700. Additionally, the treatment system1700 includes an imaging system 1716 (e.g., a camera) that capturesimages of the eye 1. The controller 1720 can receive and process theimages from the imaging system 1716 to determine the position of thecornea 2 relative to the treatment system 1700. To compensate forchanges in the position of the cornea 2, the controller 1720 can controlthe laser beam deflector 1713 to adjust the scanned laser beam and causethe spot pattern to be applied to the desired areas of the cornea 2. Assuch, the imaging system 1716 and the controller 1720 combine to providean eye tracking system.

Meanwhile, the treatment system 1800 shown in FIG. 18 includes a UV(e.g., UVA) laser source 1810, a beam expander 1811, a focusing lens1812, a diffractive beam shaper 1813, and a laser beam deflector 1814.The laser source 1810 may be implemented with a light amplitudemodulator (either internal or external to the laser source 1810). Thelaser beam from the laser source 1810 is directed to the beam expander1811 and the resulting expanded beam is directed to the focusing lens1812 and the diffractive beam shaper 1813 (e.g., flattop generator, ringgenerator, or custom shape generator). The laser beam deflector 1814receives and directs the laser beam from the diffractive beam shaper1813 to the cornea 2. As such, a laser beam spot of desired size andshape is generated at the surface of the cornea 2. Further embodimentsmay optionally employ additional lenses and beam shaper devices.

Like the treatment system 1700, the treatment system 1800 includes acontroller 1820 that may control aspects of the treatment system 1800.Additionally, the treatment system 1800 includes an imaging system 1816(e.g., a camera) that captures images of the eye 1. The controller 1820can receive and process the images from the imaging system 1816 todetermine the position of the cornea 2 relative to the treatment system1800. To compensate for changes in the position of the cornea 2, thecontroller 1820 can control the laser beam deflector 1814 to adjust thescanned laser beam and cause the spot pattern to be applied to thedesired areas of the cornea 2. As such, the imaging system 1816 and thecontroller 1820 combine to provide an eye tracking system.

In general, cross-linking treatment systems employing a laser lightsource can deliver more sophisticated and sharper photoactivating lightpatterns. As described above, embodiments can employ XY scanners,diffractive multi-beam splitters, and diffractive beam shapers toachieve the desired patterns.

As also described above, photoactivating light patterns from laser-basedtreatment systems can be optimized to achieve clinical efficacy and adesired treatment objective (e.g., refractive correction) based onparticular eye parameters for individual subjects. Optimized laser-basedtreatment system can precisely control the shape of a treatment zone andlocal strength for a patient-specific treatment pattern. Advantageously,optimized laser-based treatment systems can enhance cross-linking byefficiently use cross-linking agent and ambient oxygen based onphotochemical kinetic reactions. Indeed, such treatment systems can makeit unnecessary to have hyperoxic condition during treatment, i.e., anexternal gas source, treatment masks, etc. are not required to supplysupplemental concentrated oxygen.

As described above, according to some aspects of the present disclosure,some or all of the steps of the above-described and illustratedprocedures can be automated or guided under the control of a controller.Generally, the controllers may be implemented as a combination ofhardware and software elements. The hardware aspects may includecombinations of operatively coupled hardware components includingmicroprocessors, logical circuitry, communication/networking ports,digital filters, memory, or logical circuitry. The controller may beadapted to perform operations specified by a computer-executable code,which may be stored on a computer readable medium.

As described above, the controller may be a programmable processingdevice, such as an external conventional computer or an on-board fieldprogrammable gate array (FPGA), application specific integrated circuits(ASIC), or digital signal processor (DSP), that executes software, orstored instructions. In general, physical processors and/or machinesemployed by embodiments of the present disclosure for any processing orevaluation may include one or more networked or non-networked generalpurpose computer systems, microprocessors, field programmable gatearrays (FPGA's), application specific integrated circuits (ASIC),digital signal processors (DSP's), micro-controllers, and the like,programmed according to the teachings of the example embodiments of thepresent disclosure, as is appreciated by those skilled in the computerand software arts. The physical processors and/or machines may beexternally networked with the image capture device(s), or may beintegrated to reside within the image capture device. Appropriatesoftware can be readily prepared by programmers of ordinary skill basedon the teachings of the example embodiments, as is appreciated by thoseskilled in the software art. In addition, the devices and subsystems ofthe example embodiments can be implemented by the preparation ofapplication-specific integrated circuits or by interconnecting anappropriate network of conventional component circuits, as isappreciated by those skilled in the electrical art(s). Thus, the exampleembodiments are not limited to any specific combination of hardwarecircuitry and/or software.

Stored on any one or on a combination of computer readable media, theexample embodiments of the present disclosure may include software forcontrolling the devices and subsystems of the example embodiments, fordriving the devices and subsystems of the example embodiments, forenabling the devices and subsystems of the example embodiments tointeract with a human user, and the like. Such software can include, butis not limited to, device drivers, firmware, operating systems,development tools, applications software, and the like. Such computerreadable media further can include the computer program product of anembodiment of the present disclosure for performing all or a portion (ifprocessing is distributed) of the processing performed inimplementations. Computer code devices of the example embodiments of thepresent disclosure can include any suitable interpretable or executablecode mechanism, including but not limited to scripts, interpretableprograms, dynamic link libraries (DLLs), Java classes and applets,complete executable programs, and the like. Moreover, parts of theprocessing of the example embodiments of the present disclosure can bedistributed for better performance, reliability, cost, and the like.

Common forms of computer-readable media may include, for example, afloppy disk, a flexible disk, hard disk, magnetic tape, any othersuitable magnetic medium, a CD-ROM, CDRW, DVD, any other suitableoptical medium, punch cards, paper tape, optical mark sheets, any othersuitable physical medium with patterns of holes or other opticallyrecognizable indicia, a RAM, a PROM, an EPROM, a FLASH-EPROM, any othersuitable memory chip or cartridge, a carrier wave or any other suitablemedium from which a computer can read.

While the present disclosure has been described with reference to one ormore particular embodiments, those skilled in the art will recognizethat many changes may be made thereto without departing from the spiritand scope of the present disclosure. Each of these embodiments andobvious variations thereof is contemplated as falling within the spiritand scope of the present disclosure. It is also contemplated thatadditional embodiments according to aspects of the present disclosuremay combine any number of features from any of the embodiments describedherein.

What is claimed is:
 1. A system for treating an eye, comprising: a laserlight source configured to provide photoactivating light; a scanningmirror system configured to receive the photoactivating light as a laserbeam and to move the laser beam over a cornea treated with across-linking agent; and a controller configured to provide controlsignals to programmatically control the laser light source and thescanning mirror system, the one or more control signals causing thelaser beam to visit one or more regions of the cornea via linearscanning and retracement to constitute a scan pattern, wherein thephotoactivating light causes the cross-linking agent in the one or moreexposed regions to react with oxygen to generate cross-linking activityin the one or more exposed regions, wherein the one or more controlsignals programmatically control the laser light source, such that apredetermined period of time passes between visits by the laser beam tothe one or more exposed regions, and wherein the scan pattern includesunexposed regions on all four sides of each exposed region, such thatthe scan pattern is a checkerboard pattern.
 2. The system of claim 1,wherein the light source is operable to adjust a power associated withthe laser beam, and the scan pattern is optimized according to the powerassociated with the laser beam.
 3. The system of claim 1, wherein thescanning mirror system is operable to adjust a speed of the laser beamas the laser beam moves over the cornea, and the scan pattern isoptimized according to the speed of the laser beam.
 4. The system ofclaim 1, further comprising one or more optical elements configured toreceive the photoactivating light and determine a spot size associatedwith the laser beam, wherein the scan pattern is optimized according tothe spot size associated with the laser beam.
 5. The system of claim 1,wherein the scanning mirror system includes a galvanometer pair, thegalvanometer pair including a first mirror configured to move the laserbeam along a first axis and a second mirror configured to move the laserbeam along a second axis.
 6. The system of claim 1, wherein the scanpattern causes the laser beam to visit the one or more exposed regionswhile keeping one or more adjacent regions unexposed to thephotoactivating light, and the one or more adjacent unexposed regionsprovide oxygen for diffusion into the one or more exposed regions. 7.The system of claim 1, wherein the scan pattern is defined by a pulsingof the laser beam according to a duty cycle, wherein, as the scanningmirror system scans the laser beam over the cornea, the pulsing causesthe laser beam to visit the one or more exposed regions when the laserbeam is on during the duty cycle while adjacent regions are unexposed tothe photoactivating light when the laser beam is off during the dutycycle, and the adjacent unexposed regions provide oxygen for diffusioninto the one or more exposed regions.
 8. The system of claim 7, whereinthe pulsing of the laser beam has a frequency that varies according to aposition of the laser beam in the scan pattern.
 9. The system of claim1, wherein the one or more exposed regions correspond to a plurality ofdiscrete dots defining the scan pattern.
 10. The system of claim 1,wherein linear scanning and retracement comprises at least a firsthorizontal scan line and a second horizontal scan line, the secondhorizontal scan line disposed parallel to and vertically below the firsthorizontal scan line.
 11. A method for treating an eye, comprising:generating photoactivating light with a laser light source; directingthe photoactivating light as a laser beam to a scanning mirror system;operating the scanning mirror system to cause the laser beam to moveover a cornea and visit one or more regions of the cornea via linearscanning and retracement to constitute a scan pattern, wherein thephotoactivating light causes a cross-linking agent in the one or moreexposed regions to react with oxygen to generate cross-linking activityin the one or more exposed regions, optimizing the scan pattern byprogrammatically controlling the laser light source, such that apredetermined period of time passes between visits by the laser beam tothe one or more exposed regions, and. wherein the scan pattern includesunexposed regions on all four sides of each exposed region, such thatthe scan pattern is a checkerboard pattern.
 12. The method of claim 11,wherein optimizing the scan pattern includes adjusting a powerassociated with the laser beam.
 13. The method of claim 11, whereinoptimizing the scan pattern includes adjusting a speed of the laserbeam, and the scan pattern is optimized according to the speed of thelaser beam.
 14. The method of claim 11, wherein optimizing the scanpattern includes determining a spot size associated with the laser beam.15. The method of claim 11, wherein the scanning mirror system includesa galvanometer pair, the galvanometer pair including a first mirrorconfigured to move the laser beam along a first axis and a second mirrorconfigured to move the laser beam along a second axis.
 16. The method ofclaim 11, wherein optimizing the scan pattern includes defining the scanpattern to cause the laser beam to visit the one or more exposed regionswhile keeping one or more adjacent regions unexposed to thephotoactivating light, the one or more adjacent unexposed regionsprovide oxygen for diffusion into the one or more exposed regions. 17.The method of claim 11, wherein optimizing the scan pattern includesdefining the scan pattern to pulse the laser beam according to a dutycycle, wherein, as the scanning mirror system scans the laser beam overthe cornea, the pulsing causes the laser beam to visit the one or moreexposed regions when the laser beam is on during the duty cycle whileadjacent regions are unexposed to the photoactivating light when thelaser beam is off during the duty cycle, the adjacent unexposed regionsprovide oxygen for diffusion into the one or more exposed regions. 18.The method of claim 17, wherein the pulsing of the laser beam has afrequency that varies according to a position of the laser beam in thescan pattern.
 19. The method of claim 11, wherein the one or moreexposed regions correspond to a plurality of discrete dots defining thescan pattern.
 20. The system of claim 1, wherein linear scanning andretracement comprises at least a first horizontal scan line and a secondhorizontal scan line, the second horizontal scan line disposed parallelto and vertically below the first horizontal scan line.